Answer:
8,9,10
Step-by-step explanation:
Let x-1, x and x+1 be the consecutive integers
(x-1)(x+1) = 5x + 35
x² - 1 - 5x - 35 = 0
x² - 5x - 36 = 0
x² - 9x + 4x - 36= 0
x(x - 9) + 4(x - 9) = 0
(x - 9)(x + 4) = 0
x = 9, -4
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
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Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
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As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
4,400 + 17,600 = 22,000.
4,400 / 22,000 = 0.2
0.2 = 20%
The answer is A.
Hope this helped☺☺
I believe that it is 24.99 but I'm not too sure. Anyways I hope I helped!
